Formation probabilities in quantum critical chains and Casimir effect

Instituto de Física, Universidade Federal Fluminense - Av. Gal. Milton Tavares de Souza s/n, Gragoatá, 24210-346, Niterói, RJ, Brazil

Received: 7 December 2015
Accepted: 21 December 2015

Abstract

We find a connection between logarithmic formation probabilities of two disjoint intervals of quantum critical spin chains and the Casimir energy of two aligned needles in two-dimensional classical critical systems. Using this connection we provide a formula for the logarithmic formation probability of two disjoint intervals in generic (1 + 1)-dimensional critical systems. The quantity is depenedent on the full structure of the underlying conformal field theory and so useful to find the universality class of the critical system. The connection that we find also provides a very efficient numerical method to calculate the Casimir energy between needles using quantum critical chains. The agreement between numerical results performed on the critical transverse-field Ising model and the XX chain with our exact results is very good. We also comment on the mutual Rényi information of two disjoint intervals.